Circles

⭐ Important Questions

1. From point P, 10 cm from circle center O, tangent length PT = 8 cm. Find radius.
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   OT ⟂ PT (radius ⟂ tangent)\nOP² = OT² + PT²\n10² = r² + 8² => r² = 100 - 64 = 36\nr = 6 cm
2. Prove that tangents drawn from external point to circle are equal.
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   Given: Circle O, external point P, tangents PA, PB at A,B.\nOA = OB (radii)\nOA ⟂ PA, OB ⟂ PB (radius ⟂ tangent)\nIn triangles OAP and OBP:\nOA = OB, OP = OP (common)\n∠OAP = ∠OBP = 90\n=> Triangles congruent (RHS)\n=> PA = PB